Biological soft tissue consists mainly of light elements, and its composition is nearly uniform with little density variation. Traditional attenuation-based x-ray imaging cannot provide sufficient contrast for this type of materials. The cross-section of x-ray phase shift is three orders of magnitude greater than that of x-ray attenuation in soft tissue over the diagnostic energy range. Hence, x-ray phase-contrast imaging is sensitive to subtle features especially micro-structures of soft tissue and offers superior contrast for analyses of various normal and diseased conditions. X-ray phase-contrast imaging approaches face challenges in biomedical applications. Analyzer-based phase- contrast imaging requires monochromatic x-rays and high-precision crystals, being limited to the synchrotron radiation facility. Propagation-based imaging suffers from a low photon flux of a micro-focus x-ray tube. Grating-based phase-contrast imaging is a recent breakthrough. However, two main obstacles for this paradigm shift are (1) the large-area gratings of small periods and high aspects and (2) the long time needed for data acquisition. Technically, it is rather difficult to make large gratings especially when x-ray energy is high. Theoretically, it is extremely complicated to model the propagation of x-rays through large gratings from a point x-ray source. In this project, we will establish two enabling innovations that are (1) interior phase contrast tomography for accurate region of interest (ROI) reconstruction and (2) few-view phase-contrast reconstruction without phase-stepping for accelerated data acquisition and minimized radiation dose. The synergistic combination of these innovations will define a new frontier of x-ray phase-contrast tomography. Although the conventional wisdom is that grating-based phase-contrast tomography must use sufficiently large gratings to cover an object and capture projections completely, our main innovative thinking is to target theoretically exact reconstruction over an ROI from truncated data collected with relatively small gratings. It is underlined that the grating-based phase-contrast interior reconstruction takes truncated differential projections, while the typical interior reconstruction assumes truncated direct projections. Another new idea for this project is to utilize the reweighted L1 norm for fewer-view image reconstruction. The overall goal of this project is to establish x-ray-grating-based interior tomography theory, develop the associated few-view reconstruction methods and system without phase stepping, and promote its biomedical applications. The proposed technology will be characterized in numerical simulation and phantom experiments, and applied for musculoskeletal imaging in an animal model. Upon the completion of this project, the proposed grating-based system will have achieved 30m resolution, shortened scanning time, and reduced radiation dose over a 3cm- diameter ROI, outperforming micro-CT in terms of contrast resolution yet delivering comparable ROI image quality relative to that of conventional grating-based phase-contrast tomography.